You have to clear the third Tetris Road for this achievement.
To get to this, on the main menu:
2nd option (Xbox Live)
3rd option (Create a Session)
Top left option, set it to the 2nd option from the top, which is Tetris Road.
Then select the top most option. This will search, come to a miniature lobby, and then load the game with a 15 second countdown.
To play this mode, you must have completed the previous Tetris road, which means you will have the following achievement:
Scroll down the Tetris Road list to the third option (Grand Road).
You have 10 stages in this road:
1) Target - Remove all of the gameplay area's highlighted tetris squares. 3 areas to remove in 2 minutes
2) Tetris - Get 4 tetrises in 1 minute 40 seconds
3) Big - Get 20 lines in 1 minute 40 seconds
4) Eraser - Remove 5 specific lines in 2 minutes
5) Cycle - Get a Single, Double, Triple, & a Tetris, in any order (2 minute time limit). I recommend doing the Double last so that you qualify for the EX stage.
6) Level Star - get 20 lines in 90 seconds
7) Target - Remove all of the gameplay area's highlted tetris squares. 3 area to remove in 3 minutes.
8) Triple - Get 5 Triples in 1 minute 40 seconds
9) Eraser - Get 4 specified lines in 90 seconds
10) Level Star - Get 20 lines in 80 seconds.
If you complete these, you'll get this achievement, HOWEVER, there is one more achievement you can get in this road...Note: If you fail the EX stage, and you haven't got the achievement, the achievement for completing the road will not unlock, and you'll have to do it again.
If you finish Stage 5 (Cycle) or Stage 10 (Level Star) with a double line clear, you'll get the EX stage...
EX) Level Star - Get 20 lines in 70 seconds.
If you manage to complete the EX stage, you get the following achievement: